The production of aspheres is carried out in two steps: initially by grinding or turning in order to create the shape and subsequently by polishing in order to achieve the required surface quality.
In the prior art, both processing steps are performed by means of grinding, polishing or turning machines which are controlled by computer numerical control (“CNC”).
In the case of grinding, the tool spindle is aligned horizontally, parallel with the y-axis and at a right angle in relation to the workpiece spindle. The workpiece is affixed onto a support called a spike. The support is clamped into the workpiece spindle. Both tool and workpiece are rotated by means of the spindles. The workpiece can be driven upwards and downwards parallel with the z-axis. The tool can be moved, on one hand, to the front and to the back parallel with the y-axis in order to adjust it to the center of the workpiece and, on the other hand, to the left and to the right parallel to the x-axis in order to perform the processing procedure.
Initially, the grinding tool is a cylindrical grinding disk, where the grinding surface is the cylinder barrel. Diamonds are applied on it in a metal bond or a plastic bond. The grinding disk is formed to a narrow spherical section where the highest or thickest point is located in the midplane of the disk. For an exact processing procedure, it is mandatory always to grind using the highest point of the grinding disk. There is a danger that by wearing down a cavity forms instead of the highest point, both borders of the cavity touching the workpiece. Additionally, the grinding can be impaired by an unbalance of the grinding disk. In order to avoid both said sources of error, the grinding disk is trued after mounting it. For this, a so-called truing stone is glued onto a spike and clamped instead of the workpiece to be grinded. The grinding disk is located exactly perpendicular above the truing stone, the center of its spherical section, i.e., the virtual center of the associated sphere, lying on the elongation of the tool's axis. The grinding disk is then driven along the z-axis into the truing stone very slowly while both truing stone and grinding disk are rotating. By appropriately selecting the hardness of the stone and the rotation speeds both the stone and the disk are worn down. The result is a ball-shaped cavity in the stone and a spherical section shape of the grinding disk. Because of the mechanical and geometrical conditions, the highest point of the grinding disk is located exactly in the rotational center of the truing stone.
The grinding procedure is performed by driving the tool in x-direction across the diameter of the workpiece. During the drive, the desired shape of the workpiece is created by setting the z-position of the workpiece. For this purpose, the path is divided into small line segments for which x-values for the tool and z-values for the workpiece are delivered via a CNC program. The tool's y-position is determined by the truing procedure in a way such that the center of the grinding disk, i.e. its highest point, is running across the rotational center of the workpiece and stays constant during the processing procedure. Thus, the processing can be understood as a radial section through the workpiece, wherein the grinding disk is abstracted as a circle.
For the processing procedure, it is important that the positions of all three axes are defined exactly. The x-axis is adjusted to the greatest possible extent by the manufacturer so that, at an x-value provided by the factory, the axis of the grinding disk is standing above the axis of the workpiece. If this is not the case an error in shape results, from which the false position must be recognized and corrected manually. For this, a sample piece is processed as a general rule. The position of the z-axis must be determined by touching and merely gives the thickness of the workpiece, which can be remeasured directly in general. The position of the y-axis is, similar to the x-axis, adjusted to the greatest possible extent by the manufacturer. However, because the grinding disk is attached in y-direction and tightened a mechanical tolerance always results. Only detaching and re-attaching results in a change of the y-position. If the highest point of the tool is not running across the center of the workpiece exactly, a different point not exactly known is touching the workpiece, whereby an additional error in shape of the workpiece results. The false position with respect to the y-axis is corrected by short retruing.
This known method is not suitable for processing workpieces if an area in the middle of the workpieces, given by the radius of the grinding disk, can not be processed, for example because of unremovable parts in this central area, for example a bump.
For CNC turning, a small plate—the cutting insert—which can be turned around and contains the actual cutting edge, is screwed onto the turning chisel. In order to increase durability of the insert, its edges are chamfered to a round shape. If viewed from above, the radius between the edge running parallel with the rotation axis of the workpiece and the edge running perpendicularly is called cutting edge radius. This is the area of the cutting insert that is directly engaged. For exactly processing it is important to know exactly the cutting edge radius or the deviation from the ideal shape, respectively. In particular when turning cones or more complex shapes as spheres or aspheres, one has to pay attention to the fact that the chisel has to be set in further than would be necessary with a non-chamfered cutting tip because of said radius. Modern CNC turning machines allow entering the cutting edge radius and adjust the CNC program appropriately. It is assumed therein that the radius is kept exactly, i.e. that there is no deviation from the ideal shape.
This procedure reduces the possible accuracy of processing.
For measuring rotationally symmetric bodies, tactile measuring using profilometers is used among other methods. For this purpose, a caliper having a ruby ball or a diamond tip is drawn across the workpiece and the movement of the caliper is calculationally converted to an elevation profile. After subtracting the specified shape, one obtains the error of the measured object. The caliper normally is a right angle consisting of two sticks, at whose vertical, lower end the ruby ball or the diamond tip is located respectively, and whose vertical stick is suspended in a seesaw. The tilt angle of the seesaw is measured and the position of the measuring ball or tip, respectively, and furthermore the shape of the workpiece are calculated. In the case of rotationally symmetric workpieces, a run across the diameter of the workpiece is performed meanwhile. The z-position of the measuring system is constant in the meantime, it is drawn in one direction only.
This method is not feasible for workpieces having a central bump or hole.
Due to the principle of the method, the absolute position of the workpiece in x-direction is unknown after a tactile measurement. In particular, the measuring system is driven away for each measurement to be able to take out the workpiece so that a constant position of the measuring system is not given across several measurements. One of the aims of analyzing the measurement therefore is to determine the position of the workpiece in relation to the x-axis and, in particular for rotationally symmetric workpieces, to determine the center. One possibility consists in approximately solving a system of equations using the method of least squares.
This implies that the specified shape of the workpiece can be described appropriately analytically. However, this is impossible especially for aspheres.